arXiv research

Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.

New algorithm guarantees performance on noisy data.

Wavelet-based online learning adapts to noisy Besov spaces with high probability.

A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with individual guarantees. We close this gap by introducing a black-box modification to …

This paper addresses the problem of prediction with expert advice for outcomes in a geodesic space with non-positive curvature in the sense of Alexandrov. Via geometric considerations, and in particular the notion of barycenters, we extend to this setting the definition and analysis of the classical exponentially weigh…

The paper optimizes distribution estimation with high probability in Kullback-Leibler divergence.

The paper explores trade-offs between regret and variance in online learning algorithms.

Extends online learning to metric spaces using exponential weights.

Time series forecasting is widely used in a multitude of domains. In this paper, we present four models to predict the stock price using the SPX index as input time series data. The martingale and ordinary linear models require the strongest assumption in stationarity which we use as baseline models. The generalized li…

New bounds for online convex optimization between stochastic and adversarial settings.

The paper advances U-statistics in dependent settings, improving spectral estimation and goodness-of-fit tests.

FOLKLORE algorithm speeds up online multiclass logistic regression.

A new algorithm reduces online exp-concave optimization runtime.

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much more fine grained control over prediction, but at the same time present novel c…

We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling inequa…

This paper identifies knot projections with reductivity two.

This paper classifies instantons with closed reductions and provides examples of non-closed reductions.

We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,Γ) where K is a Kaehler manifold and Γa discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invari…

In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We sh…

Two reduction schemes for symplectic manifolds are shown equivalent.

Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.

The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.

We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to Kähler reduction by considering the Kähler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained by $S^1$ reduction of standard Sasakian spheres.

Study characterizes naturally reductive metrics on homogeneous manifolds.

Abstract: Generalized reduction methods for symmetries in graded geometry.

In this note we give conditions which ensure the reduction of a symplectic connection in the process of a Marsden-Weinstein reduction and of the reduction of a presymplectic manifold.

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to descr…

The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.

This paper extends symplectic reduction to cosymplectic groupoids and explores their properties.

Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $H\subset G$ be a complex reductive subgroup which is not necessarily connected, and let $E_H\subset E_G$ be a holomorphic reduction of s…

A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dime…

New definition of naturally reductive Finsler manifolds using geodesic graphs.

Survey of Lagrangian reduction for discrete mechanical systems.

New method corrects missing data bias in dimension reduction.

Paper compares Lagrangian reduction methods for rigid body systems.

The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.

The paper simplifies symmetries in complex geometric structures.

A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the na…

The paper explores polysymplectic structures and their reductions in field theories.

We complete the reduction scheme in the whole LP category, introduced in [7] to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category and analyze the Noether theorem on LP-bundles, the relationship with Hamiltonian reduction by stages an…

Develops Marsden-Meyer-Weinstein reduction for $k$-contact field theories.

Paper shows spectra can't distinguish naturally reductive manifolds.

The paper explores reductions of self-dual conformal structure equations.

In the present paper we study naturally reductive homogeneous $(α,β)$-metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous $(α,β)$-metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler …

Abstract reviews symmetry and reduction in dynamical systems.

We discuss the use of Dirac structures to obtain a better understanding of the geometry of a class of optimal control problems and their reduction by symmetries. In particular we will show how to extend the reduction of Dirac structures recently proposed by Yoshimura and Marsden [Yo09] to describe the reduction of a cl…

This work extends reduction processes for nonholonomic discrete mechanical systems.

We define reduction of locally conformal Kaehler manifolds, considered as conformal Hermitian manifolds, and we show its equivalence with an unpublished construction given by Biquard and Gauduchon. We show the compatibility between this reduction and Kaehler reduction of the universal cover. By a recent result of Kamis…